2019 Scrambler Option 719, 2013 K1600GTL,
The only thing connected to the 10A circuit with the key turned off is the electronic control module. and afterwards, everything else controlled by and connected to the ecu. The key energizes the ECU and the ECU is holding the main relay closed on its own, probably through software. One minute may be how long it's programmed to stay on. I don't know. Try disconnecting the other items connected to the ECU. I'd start with the ABS module. I assume your voltmeter is reading the battery directly?